Related papers: Progress on two-loop non-propagator integrals
We present a formalism for the calculation of multi-particle one-loop amplitudes, valid for an arbitrary number N of external legs, and for massive as well as massless particles. A new method for the tensor reduction is suggested which…
In this presentation, we review the general features of integrand-reduction techniques, with a particular focus on their generalization beyond one loop. We start with a brief discussion of the one-loop scenario, a case in which…
The existence of a finite basis of algebraically independent one-loop integrals has underpinned important developments in the computation of one-loop amplitudes in field theories and gauge theories in particular. We give an explicit…
To entirely determine the resulting functions of one-loop integrals it is necessary to find the correct analytic continuation to all relevant kinematical regions. We argue that this continuation procedure may be performed in a general and…
We introduce a novel structure for Feynman integrals, reformulating them as integrals over a small set of parameters with a fully controllable integrand. The integrand closely resembles one-loop Feynman integrals, and they are very easy to…
We calculate the three-loop master integrals contributing to the three-loop five-point amplitude on the special Coulomb branch of $\mathcal{N}=4$ SYM theory. For the genuine pentagon integrals, we follow the approach of Ref. [JHEP 12 (2025)…
We evaluated all two-loop conformal integrals of scalar half-BPS six-point functions in $\mathcal{N} = 4$ SYM restricted to a configuration where all points lie on a line. Moreover, we also computed some of these integrals in the…
Planar L-loop maximally helicity violating amplitudes in N = 4 supersymmetric Yang-Mills theory are believed to possess the remarkable property of satisfying iteration relations in L. We propose a simple new method for studying the…
Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…
We consider the analytic calculation of a two-loop non-planar three-point function which contributes to the two-loop amplitudes for $t \bar{t}$ production and $\gamma \gamma$ production in gluon fusion through a massive top-quark loop. All…
In the present paper the two and three point functions which occur at the study of the various physical processes are considered. The investigation has dan in the framework of the perturbative theory at the one loop level. The general and…
Using the results recently obtained for computing integrals over (non-minimal) pure spinor superspace, we compute the coefficient of the massless two-loop four-point amplitude from first principles. Contrasting with the mathematical…
We report on the advances in the calculation of the two-loop scattering amplitudes for five-particle processes with one off-shell leg. Focusing on the production of a Higgs boson in association with a bottom quark pair, we outline how the…
Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…
The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…
Recent Developments in computing very specific helicity amplitudes in two loop QCD are presented. The techniques focus upon the singular structure of the amplitude rather than on a diagramatic and integration approach
The infrared exponentiation properties of dimensionally-regularized multi-loop scattering amplitudes are typically hidden at the level of the integrand, materializing only after integral evaluation. We address this long-standing problem by…
In this paper I review some old and new works on the computation of two-loop 4-particle amplitude in superstring theory. I also present the proof by Iengo, showing the vanishing of the term related to the two-loop correction to the $R^4$…
An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…
We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop…